If you're looking to understand photonic crystals, this systematic, rigorous, and pedagogical introduction is a must. Here you'll find intuitive analytical and semi-analytical models applied to complex and practically relevant photonic crystal structures. You will also be shown how to use various analytical methods borrowed from quantum mechanics, such as perturbation theory, asymptotic analysis, and group theory, to investigate many of the limiting properties of photonic crystals which are otherwise difficult to rationalize using only numerical simulations. An introductory review of nonlinear guiding in photonic lattices is also presented, as are the fabrication and application of photonic crystals. In addition, end-of-chapter exercise problems with detailed analytical and numerical solutions allow you to monitor your understanding of the material presented. This accessible text is ideal for researchers and graduate students studying photonic crystals in departments of electrical engineering, physics, applied physics and mathematics.
Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals at the Department of Engineering Physics at Ecole Polytechnique de Montreal, Canada. In 2005 he was awarded a fellowship from the Japanese Society for Promotion of Science, and he is a member of the Optical Society of America. Jianke Yang is Professor of Applied Mathematics at the University of Vermont, USA. He is a member of the Optical Society of America and the Society of Industrial and Applied Mathematics.
1. Introduction; 2. Hamiltonian formulation of Maxwell's equations (frequency consideration); 3. 1D Photonic crystals - multilayer stacks; 4. Bandgap guidance in the planar photonic crystal waveguides; 5. Hamiltonian formuation of Maxwell equations for waveguides (propagation constant consideration); 6. 2D photonic crystals; 7. Quasi-2D photonic crystals; 8. Nonlinear effects and gap-solution formation in periodic media; 9. Problem solution.